Summary

The work is devoted to obtaining conditions of Noether for integral equations of the convolutional
type with polynomial kernels in the normal and singular cases, to studying the conditions of their
normal solvability and the properties of solutions constructed there. The equivalent singular
integral equations with the Cauchy kernel at the real axis for these integral equations were
constructed here. Studying of Noether conditions and conditions of the existence of solutions
in the normal and singular cases was made here basing on Noether conditions and conditions
of the existence of solutions for singular integral equations with Cauchy kernel. The conditions
of solvability for a singular integral equation with Cauchy kernel in the singular case were also
established here basing on the conditions of the solvability for the equivalent Rieman boundary
problem in the singular case. A very important role there played integral representations for
functions and derivatives of them, which are analytical in the upper and lower half planes of the
complex plane that permitted to transform Rieman boundary problems into singular integral
equations with Cauchy kernel. Spaces of solutions of integral equations of the convolutional
type considered here in normal and singular cases were defined and studyed in that work. The
analogous results for some systems of the integral equations of the convolutional type are also
obtained here.